Based on the addressing capability, there are three classifications of DMA (Direct Memory Access) controllers.

1. Single-Mode DMA Controller:
A single-mode DMA controller can access only a single block of memory at a time. It is capable of transferring data between a device and memory, or between two devices, but it can only access a specific block of memory during the transfer. Once the transfer is complete, the controller releases the bus and another device can take control.

2. Demand-Mode DMA Controller:
A demand-mode DMA controller is capable of accessing multiple blocks of memory during a transfer. It can dynamically allocate and release memory blocks as required by the devices. This allows for more efficient use of memory resources and reduces the need for continuous bus control. The controller can transfer data between a device and memory, or between two devices, without releasing control of the bus.

3. Block-Mode DMA Controller:
A block-mode DMA controller is an advanced version of the demand-mode DMA controller. It can perform block transfers of data between a device and memory, or between two devices, without releasing control of the bus. This means that it can transfer a block of data from one location to another without having to pause or release the bus between each transfer. This significantly improves the efficiency of the data transfer process.

In summary, the three classifications of DMA controllers based on addressing capability are single-mode, demand-mode, and block-mode DMA controllers. Each type offers different levels of flexibility and efficiency in accessing and transferring data between devices and memory.